{-# LANGUAGE CPP #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE DefaultSignatures #-}
{-# LANGUAGE UndecidableInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FunctionalDependencies #-}

#ifdef TRUSTWORTHY
{-# LANGUAGE Trustworthy #-} -- vector, hashable
#endif

#if __GLASGOW_HASKELL__ >= 711
{-# OPTIONS_GHC -fno-warn-redundant-constraints #-}
#endif

#ifndef MIN_VERSION_base
#define MIN_VERSION_base(x,y,z) 1
#endif

#ifndef MIN_VERSION_containers
#define MIN_VERSION_containers(x,y,z) 1
#endif
-------------------------------------------------------------------------------
-- |
-- Module      :  Control.Lens.Indexed
-- Copyright   :  (C) 2012-16 Edward Kmett
-- License     :  BSD-style (see the file LICENSE)
-- Maintainer  :  Edward Kmett <ekmett@gmail.com>
-- Stability   :  provisional
-- Portability :  Rank2Types
--
-- (The classes in here need to be defined together for @DefaultSignatures@ to work.)
-------------------------------------------------------------------------------
module Control.Lens.Indexed
  (
  -- * Indexing
    Indexable(..)
  , Conjoined(..)
  , Indexed(..)
  , (<.), (<.>), (.>)
  , selfIndex
  , reindexed
  , icompose
  , indexing
  , indexing64
  -- * Indexed Functors
  , FunctorWithIndex(..)
  -- * Indexed Foldables
  , FoldableWithIndex(..)
  -- ** Indexed Foldable Combinators
  , iany
  , iall
  , inone, none
  , itraverse_
  , ifor_
  , imapM_
  , iforM_
  , iconcatMap
  , ifind
  , ifoldrM
  , ifoldlM
  , itoList
  -- * Converting to Folds
  , withIndex
  , asIndex
  -- * Restricting by Index
  , indices
  , index
  -- * Indexed Traversables
  , TraversableWithIndex(..)
  -- * Indexed Traversable Combinators
  , ifor
  , imapM
  , iforM
  , imapAccumR
  , imapAccumL
  -- * Indexed Folds with Reified Monoid
  , ifoldMapBy
  , ifoldMapByOf
  -- * Indexed Traversals with Reified Applicative
  , itraverseBy
  , itraverseByOf
  ) where

import Control.Applicative
import Control.Applicative.Backwards
import Control.Comonad.Cofree
import Control.Comonad.Trans.Traced
import Control.Monad (void, liftM)
import Control.Monad.Trans.Identity
import Control.Monad.Trans.Reader
import Control.Monad.Trans.State.Lazy as Lazy
import Control.Monad.Free
import Control.Lens.Fold
import Control.Lens.Getter
import Control.Lens.Internal.Fold
import Control.Lens.Internal.Indexed
import Control.Lens.Internal.Level
import Control.Lens.Internal.Magma
import Control.Lens.Setter
import Control.Lens.Traversal
import Control.Lens.Type
import Data.Array (Array)
import qualified Data.Array as Array
import Data.Foldable
import Data.Functor.Compose
import Data.Functor.Contravariant
import Data.Functor.Product
import Data.Functor.Reverse
import Data.Hashable
import Data.HashMap.Lazy as HashMap
import Data.IntMap as IntMap
import Data.Ix (Ix)
import Data.List.NonEmpty as NonEmpty
import Data.Map as Map
import Data.Monoid hiding (Product)
import Data.Profunctor.Unsafe
import Data.Reflection
import Data.Sequence hiding ((:<), index)
import Data.Tree
import Data.Tuple (swap)
import Data.Vector (Vector)
import qualified Data.Vector as V
import Prelude

#if !(MIN_VERSION_base(4,8,0))
import Data.Traversable (sequenceA)
#endif

#ifdef HLINT
{-# ANN module "HLint: ignore Use fmap" #-}
#endif

infixr 9 <.>, <., .>

-- $setup
-- >>> :set -XNoOverloadedStrings
-- >>> import Control.Lens

-- | Compose an 'Indexed' function with a non-indexed function.
--
-- Mnemonically, the @<@ points to the indexing we want to preserve.
--
-- >>> let nestedMap = (fmap Map.fromList . Map.fromList) [(1, [(10, "one,ten"), (20, "one,twenty")]), (2, [(30, "two,thirty"), (40,"two,forty")])]
-- >>> nestedMap^..(itraversed<.itraversed).withIndex
-- [(1,"one,ten"),(1,"one,twenty"),(2,"two,thirty"),(2,"two,forty")]
(<.) :: Indexable i p => (Indexed i s t -> r) -> ((a -> b) -> s -> t) -> p a b -> r
(<.) f g h = f . Indexed $ g . indexed h
{-# INLINE (<.) #-}

-- | Compose a non-indexed function with an 'Indexed' function.
--
-- Mnemonically, the @>@ points to the indexing we want to preserve.
--
-- This is the same as @('.')@.
--
-- @f '.' g@ (and @f '.>' g@) gives you the index of @g@ unless @g@ is index-preserving, like a
-- 'Prism', 'Iso' or 'Equality', in which case it'll pass through the index of @f@.
--
-- >>> let nestedMap = (fmap Map.fromList . Map.fromList) [(1, [(10, "one,ten"), (20, "one,twenty")]), (2, [(30, "two,thirty"), (40,"two,forty")])]
-- >>> nestedMap^..(itraversed.>itraversed).withIndex
-- [(10,"one,ten"),(20,"one,twenty"),(30,"two,thirty"),(40,"two,forty")]
(.>) :: (st -> r) -> (kab -> st) -> kab -> r
(.>) = (.)
{-# INLINE (.>) #-}

-- | Use a value itself as its own index. This is essentially an indexed version of 'id'.
--
-- Note: When used to modify the value, this can break the index requirements assumed by 'indices' and similar,
-- so this is only properly an 'IndexedGetter', but it can be used as more.
--
-- @
-- 'selfIndex' :: 'IndexedGetter' a a b
-- @
selfIndex :: Indexable a p => p a fb -> a -> fb
selfIndex f a = indexed f a a
{-# INLINE selfIndex #-}

-- | Remap the index.
reindexed :: Indexable j p => (i -> j) -> (Indexed i a b -> r) -> p a b -> r
reindexed ij f g = f . Indexed $ indexed g . ij
{-# INLINE reindexed #-}

-- | Composition of 'Indexed' functions.
--
-- Mnemonically, the @\<@ and @\>@ points to the fact that we want to preserve the indices.
--
-- >>> let nestedMap = (fmap Map.fromList . Map.fromList) [(1, [(10, "one,ten"), (20, "one,twenty")]), (2, [(30, "two,thirty"), (40,"two,forty")])]
-- >>> nestedMap^..(itraversed<.>itraversed).withIndex
-- [((1,10),"one,ten"),((1,20),"one,twenty"),((2,30),"two,thirty"),((2,40),"two,forty")]
(<.>) :: Indexable (i, j) p => (Indexed i s t -> r) -> (Indexed j a b -> s -> t) -> p a b -> r
f <.> g = icompose (,) f g
{-# INLINE (<.>) #-}

-- | Composition of 'Indexed' functions with a user supplied function for combining indices.
icompose :: Indexable p c => (i -> j -> p) -> (Indexed i s t -> r) -> (Indexed j a b -> s -> t) -> c a b -> r
icompose ijk istr jabst cab = istr . Indexed $ \i -> jabst . Indexed $ \j -> indexed cab $ ijk i j
{-# INLINE icompose #-}

-------------------------------------------------------------------------------
-- Restricting by index
-------------------------------------------------------------------------------

-- | This allows you to filter an 'IndexedFold', 'IndexedGetter', 'IndexedTraversal' or 'IndexedLens' based on a predicate
-- on the indices.
--
-- >>> ["hello","the","world","!!!"]^..traversed.indices even
-- ["hello","world"]
--
-- >>> over (traversed.indices (>0)) Prelude.reverse $ ["He","was","stressed","o_O"]
-- ["He","saw","desserts","O_o"]
indices :: (Indexable i p, Applicative f) => (i -> Bool) -> Optical' p (Indexed i) f a a
indices p f = Indexed $ \i a -> if p i then indexed f i a else pure a
{-# INLINE indices #-}

-- | This allows you to filter an 'IndexedFold', 'IndexedGetter', 'IndexedTraversal' or 'IndexedLens' based on an index.
--
-- >>> ["hello","the","world","!!!"]^?traversed.index 2
-- Just "world"
index :: (Indexable i p, Eq i, Applicative f) => i -> Optical' p (Indexed i) f a a
index j f = Indexed $ \i a -> if j == i then indexed f i a else pure a
{-# INLINE index #-}


-------------------------------------------------------------------------------
-- FunctorWithIndex
-------------------------------------------------------------------------------

-- | A 'Functor' with an additional index.
--
-- Instances must satisfy a modified form of the 'Functor' laws:
--
-- @
-- 'imap' f '.' 'imap' g ≡ 'imap' (\\i -> f i '.' g i)
-- 'imap' (\\_ a -> a) ≡ 'id'
-- @
class Functor f => FunctorWithIndex i f | f -> i where
  -- | Map with access to the index.
  imap :: (i -> a -> b) -> f a -> f b
  default imap :: TraversableWithIndex i f => (i -> a -> b) -> f a -> f b
  imap = iover itraversed
  {-# INLINE imap #-}

  -- | The 'IndexedSetter' for a 'FunctorWithIndex'.
  --
  -- If you don't need access to the index, then 'mapped' is more flexible in what it accepts.
  imapped :: IndexedSetter i (f a) (f b) a b
  imapped = conjoined mapped (isets imap)
  {-# INLINE imapped #-}

-------------------------------------------------------------------------------
-- FoldableWithIndex
-------------------------------------------------------------------------------

-- | A container that supports folding with an additional index.
class Foldable f => FoldableWithIndex i f | f -> i where
  --
  -- | Fold a container by mapping value to an arbitrary 'Monoid' with access to the index @i@.
  --
  -- When you don't need access to the index then 'foldMap' is more flexible in what it accepts.
  --
  -- @
  -- 'foldMap' ≡ 'ifoldMap' '.' 'const'
  -- @
  ifoldMap :: Monoid m => (i -> a -> m) -> f a -> m
#ifndef HLINT
  default ifoldMap :: (TraversableWithIndex i f, Monoid m) => (i -> a -> m) -> f a -> m
  ifoldMap = ifoldMapOf itraversed
  {-# INLINE ifoldMap #-}
#endif

  -- | The 'IndexedFold' of a 'FoldableWithIndex' container.
  --
  -- @'ifolded' '.' 'asIndex'@ is a fold over the keys of a 'FoldableWithIndex'.
  --
  -- >>> Data.Map.fromList [(2, "hello"), (1, "world")]^..ifolded.asIndex
  -- [1,2]
  ifolded :: IndexedFold i (f a) a
  ifolded = conjoined folded $ \f -> phantom . getFolding . ifoldMap (\i -> Folding #. indexed f i)
  {-# INLINE ifolded #-}

  -- | Right-associative fold of an indexed container with access to the index @i@.
  --
  -- When you don't need access to the index then 'Data.Foldable.foldr' is more flexible in what it accepts.
  --
  -- @
  -- 'Data.Foldable.foldr' ≡ 'ifoldr' '.' 'const'
  -- @
  ifoldr   :: (i -> a -> b -> b) -> b -> f a -> b
  ifoldr f z t = appEndo (ifoldMap (\i -> Endo #. f i) t) z
  {-# INLINE ifoldr #-}

  -- | Left-associative fold of an indexed container with access to the index @i@.
  --
  -- When you don't need access to the index then 'Data.Foldable.foldl' is more flexible in what it accepts.
  --
  -- @
  -- 'Data.Foldable.foldl' ≡ 'ifoldl' '.' 'const'
  -- @
  ifoldl :: (i -> b -> a -> b) -> b -> f a -> b
  ifoldl f z t = appEndo (getDual (ifoldMap (\i -> Dual #. Endo #. flip (f i)) t)) z
  {-# INLINE ifoldl #-}

  -- | /Strictly/ fold right over the elements of a structure with access to the index @i@.
  --
  -- When you don't need access to the index then 'foldr'' is more flexible in what it accepts.
  --
  -- @
  -- 'foldr'' ≡ 'ifoldr'' '.' 'const'
  -- @
  ifoldr' :: (i -> a -> b -> b) -> b -> f a -> b
  ifoldr' f z0 xs = ifoldl f' id xs z0
    where f' i k x z = k $! f i x z
  {-# INLINE ifoldr' #-}

  -- | Fold over the elements of a structure with an index, associating to the left, but /strictly/.
  --
  -- When you don't need access to the index then 'Control.Lens.Fold.foldlOf'' is more flexible in what it accepts.
  --
  -- @
  -- 'Control.Lens.Fold.foldlOf'' l ≡ 'ifoldlOf'' l '.' 'const'
  -- @
  ifoldl' :: (i -> b -> a -> b) -> b -> f a -> b
  ifoldl' f z0 xs = ifoldr f' id xs z0
    where f' i x k z = k $! f i z x
  {-# INLINE ifoldl' #-}

-- | Return whether or not any element in a container satisfies a predicate, with access to the index @i@.
--
-- When you don't need access to the index then 'any' is more flexible in what it accepts.
--
-- @
-- 'any' ≡ 'iany' '.' 'const'
-- @
iany :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool
iany f = getAny #. ifoldMap (\i -> Any #. f i)
{-# INLINE iany #-}

-- | Return whether or not all elements in a container satisfy a predicate, with access to the index @i@.
--
-- When you don't need access to the index then 'all' is more flexible in what it accepts.
--
-- @
-- 'all' ≡ 'iall' '.' 'const'
-- @
iall :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool
iall f = getAll #. ifoldMap (\i -> All #. f i)
{-# INLINE iall #-}

-- | Return whether or not none of the elements in a container satisfy a predicate, with access to the index @i@.
--
-- When you don't need access to the index then 'none' is more flexible in what it accepts.
--
-- @
-- 'none' ≡ 'inone' '.' 'const'
-- 'inone' f ≡ 'not' '.' 'iany' f
-- @
inone :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Bool
inone f = not . iany f
{-# INLINE inone #-}

-- | Determines whether no elements of the structure satisfy the predicate.
--
-- @
-- 'none' f ≡ 'not' '.' 'any' f
-- @
none :: Foldable f => (a -> Bool) -> f a -> Bool
none f = not . Data.Foldable.any f
{-# INLINE none #-}

-- | Traverse elements with access to the index @i@, discarding the results.
--
-- When you don't need access to the index then 'traverse_' is more flexible in what it accepts.
--
-- @
-- 'traverse_' l = 'itraverse' '.' 'const'
-- @
itraverse_ :: (FoldableWithIndex i t, Applicative f) => (i -> a -> f b) -> t a -> f ()
itraverse_ f = getTraversed #. ifoldMap (\i -> Traversed #. void . f i)
{-# INLINE itraverse_ #-}

-- | Traverse elements with access to the index @i@, discarding the results (with the arguments flipped).
--
-- @
-- 'ifor_' ≡ 'flip' 'itraverse_'
-- @
--
-- When you don't need access to the index then 'for_' is more flexible in what it accepts.
--
-- @
-- 'for_' a ≡ 'ifor_' a '.' 'const'
-- @
ifor_ :: (FoldableWithIndex i t, Applicative f) => t a -> (i -> a -> f b) -> f ()
ifor_ = flip itraverse_
{-# INLINE ifor_ #-}

-- | Run monadic actions for each target of an 'IndexedFold' or 'Control.Lens.IndexedTraversal.IndexedTraversal' with access to the index,
-- discarding the results.
--
-- When you don't need access to the index then 'Control.Lens.Fold.mapMOf_' is more flexible in what it accepts.
--
-- @
-- 'mapM_' ≡ 'imapM' '.' 'const'
-- @
imapM_ :: (FoldableWithIndex i t, Monad m) => (i -> a -> m b) -> t a -> m ()
imapM_ f = getSequenced #. ifoldMap (\i -> Sequenced #. liftM skip . f i)
{-# INLINE imapM_ #-}

-- | Run monadic actions for each target of an 'IndexedFold' or 'Control.Lens.IndexedTraversal.IndexedTraversal' with access to the index,
-- discarding the results (with the arguments flipped).
--
-- @
-- 'iforM_' ≡ 'flip' 'imapM_'
-- @
--
-- When you don't need access to the index then 'Control.Lens.Fold.forMOf_' is more flexible in what it accepts.
--
-- @
-- 'Control.Lens.Fold.forMOf_' l a ≡ 'iforMOf' l a '.' 'const'
-- @
iforM_ :: (FoldableWithIndex i t, Monad m) => t a -> (i -> a -> m b) -> m ()
iforM_ = flip imapM_
{-# INLINE iforM_ #-}

-- | Concatenate the results of a function of the elements of an indexed container with access to the index.
--
-- When you don't need access to the index then 'concatMap' is more flexible in what it accepts.
--
-- @
-- 'concatMap' ≡ 'iconcatMap' '.' 'const'
-- 'iconcatMap' ≡ 'ifoldMap'
-- @
iconcatMap :: FoldableWithIndex i f => (i -> a -> [b]) -> f a -> [b]
iconcatMap = ifoldMap
{-# INLINE iconcatMap #-}

-- | Searches a container with a predicate that is also supplied the index, returning the left-most element of the structure
-- matching the predicate, or 'Nothing' if there is no such element.
--
-- When you don't need access to the index then 'find' is more flexible in what it accepts.
--
-- @
-- 'find' ≡ 'ifind' '.' 'const'
-- @
ifind :: FoldableWithIndex i f => (i -> a -> Bool) -> f a -> Maybe (i, a)
ifind p = ifoldr (\i a y -> if p i a then Just (i, a) else y) Nothing
{-# INLINE ifind #-}

-- | Monadic fold right over the elements of a structure with an index.
--
-- When you don't need access to the index then 'foldrM' is more flexible in what it accepts.
--
-- @
-- 'foldrM' ≡ 'ifoldrM' '.' 'const'
-- @
ifoldrM :: (FoldableWithIndex i f, Monad m) => (i -> a -> b -> m b) -> b -> f a -> m b
ifoldrM f z0 xs = ifoldl f' return xs z0
  where f' i k x z = f i x z >>= k
{-# INLINE ifoldrM #-}

-- | Monadic fold over the elements of a structure with an index, associating to the left.
--
-- When you don't need access to the index then 'foldlM' is more flexible in what it accepts.
--
-- @
-- 'foldlM' ≡ 'ifoldlM' '.' 'const'
-- @
ifoldlM :: (FoldableWithIndex i f, Monad m) => (i -> b -> a -> m b) -> b -> f a -> m b
ifoldlM f z0 xs = ifoldr f' return xs z0
  where f' i x k z = f i z x >>= k
{-# INLINE ifoldlM #-}

-- | Extract the key-value pairs from a structure.
--
-- When you don't need access to the indices in the result, then 'Data.Foldable.toList' is more flexible in what it accepts.
--
-- @
-- 'Data.Foldable.toList' ≡ 'Data.List.map' 'snd' '.' 'itoList'
-- @
itoList :: FoldableWithIndex i f => f a -> [(i,a)]
itoList = ifoldr (\i c -> ((i,c):)) []
{-# INLINE itoList #-}

-------------------------------------------------------------------------------
-- TraversableWithIndex
-------------------------------------------------------------------------------

-- | A 'Traversable' with an additional index.
--
-- An instance must satisfy a (modified) form of the 'Traversable' laws:
--
-- @
-- 'itraverse' ('const' 'Identity') ≡ 'Identity'
-- 'fmap' ('itraverse' f) '.' 'itraverse' g ≡ 'Data.Functor.Compose.getCompose' '.' 'itraverse' (\\i -> 'Data.Functor.Compose.Compose' '.' 'fmap' (f i) '.' g i)
-- @
class (FunctorWithIndex i t, FoldableWithIndex i t, Traversable t) => TraversableWithIndex i t | t -> i where
  -- | Traverse an indexed container.
  --
  -- @
  -- 'itraverse' ≡ 'itraverseOf' 'itraversed'
  -- @
  itraverse :: Applicative f => (i -> a -> f b) -> t a -> f (t b)
#ifndef HLINT
  default itraverse :: Applicative f => (Int -> a -> f b) -> t a -> f (t b)
  itraverse = traversed .# Indexed
  {-# INLINE itraverse #-}
#endif

  -- | The 'IndexedTraversal' of a 'TraversableWithIndex' container.
  itraversed :: IndexedTraversal i (t a) (t b) a b
  itraversed = conjoined traverse (itraverse . indexed)
  {-# INLINE itraversed #-}

-- | Traverse with an index (and the arguments flipped).
--
-- @
-- 'for' a ≡ 'ifor' a '.' 'const'
-- 'ifor' ≡ 'flip' 'itraverse'
-- @
ifor :: (TraversableWithIndex i t, Applicative f) => t a -> (i -> a -> f b) -> f (t b)
ifor = flip itraverse
{-# INLINE ifor #-}

-- | Map each element of a structure to a monadic action,
-- evaluate these actions from left to right, and collect the results, with access
-- the index.
--
-- When you don't need access to the index 'mapM' is more liberal in what it can accept.
--
-- @
-- 'mapM' ≡ 'imapM' '.' 'const'
-- @
imapM :: (TraversableWithIndex i t, Monad m) => (i -> a -> m b) -> t a -> m (t b)
imapM f = unwrapMonad #. itraverse (\i -> WrapMonad #. f i)
{-# INLINE imapM #-}

-- | Map each element of a structure to a monadic action,
-- evaluate these actions from left to right, and collect the results, with access
-- its position (and the arguments flipped).
--
-- @
-- 'forM' a ≡ 'iforM' a '.' 'const'
-- 'iforM' ≡ 'flip' 'imapM'
-- @
iforM :: (TraversableWithIndex i t, Monad m) => t a -> (i -> a -> m b) -> m (t b)
iforM = flip imapM
{-# INLINE iforM #-}

-- | Generalizes 'Data.Traversable.mapAccumR' to add access to the index.
--
-- 'imapAccumROf' accumulates state from right to left.
--
-- @
-- 'Control.Lens.Traversal.mapAccumR' ≡ 'imapAccumR' '.' 'const'
-- @
imapAccumR :: TraversableWithIndex i t => (i -> s -> a -> (s, b)) -> s -> t a -> (s, t b)
imapAccumR f s0 a = swap (Lazy.runState (forwards (itraverse (\i c -> Backwards (Lazy.state (\s -> swap (f i s c)))) a)) s0)
{-# INLINE imapAccumR #-}

-- | Generalizes 'Data.Traversable.mapAccumL' to add access to the index.
--
-- 'imapAccumLOf' accumulates state from left to right.
--
-- @
-- 'Control.Lens.Traversal.mapAccumLOf' ≡ 'imapAccumL' '.' 'const'
-- @
imapAccumL :: TraversableWithIndex i t => (i -> s -> a -> (s, b)) -> s -> t a -> (s, t b)
imapAccumL f s0 a = swap (Lazy.runState (itraverse (\i c -> Lazy.state (\s -> swap (f i s c))) a) s0)
{-# INLINE imapAccumL #-}

-------------------------------------------------------------------------------
-- Instances
-------------------------------------------------------------------------------

instance FunctorWithIndex i f => FunctorWithIndex i (Backwards f) where
  imap f  = Backwards . imap f . forwards
  {-# INLINE imap #-}

instance FoldableWithIndex i f => FoldableWithIndex i (Backwards f) where
  ifoldMap f = ifoldMap f . forwards
  {-# INLINE ifoldMap #-}

instance TraversableWithIndex i f => TraversableWithIndex i (Backwards f) where
  itraverse f = fmap Backwards . itraverse f . forwards
  {-# INLINE itraverse #-}

instance FunctorWithIndex i f => FunctorWithIndex i (Reverse f) where
  imap f = Reverse . imap f . getReverse
  {-# INLINE imap #-}

instance FoldableWithIndex i f => FoldableWithIndex i (Reverse f) where
  ifoldMap f = getDual . ifoldMap (\i -> Dual #. f i) . getReverse
  {-# INLINE ifoldMap #-}

instance TraversableWithIndex i f => TraversableWithIndex i (Reverse f) where
  itraverse f = fmap Reverse . forwards . itraverse (\i -> Backwards . f i) . getReverse
  {-# INLINE itraverse #-}

instance FunctorWithIndex () Identity where
  imap f (Identity a) = Identity (f () a)
  {-# INLINE imap #-}

instance FoldableWithIndex () Identity where
  ifoldMap f (Identity a) = f () a
  {-# INLINE ifoldMap #-}

instance TraversableWithIndex () Identity where
  itraverse f (Identity a) = Identity <$> f () a
  {-# INLINE itraverse #-}

instance FunctorWithIndex k ((,) k) where
  imap f (k,a) = (k, f k a)
  {-# INLINE imap #-}

instance FoldableWithIndex k ((,) k) where
  ifoldMap = uncurry
  {-# INLINE ifoldMap #-}

instance TraversableWithIndex k ((,) k) where
  itraverse f (k, a) = (,) k <$> f k a
  {-# INLINE itraverse #-}

-- | The position in the list is available as the index.
instance FunctorWithIndex Int []
instance FoldableWithIndex Int []
instance TraversableWithIndex Int [] where
  itraversed = traversed
  {-# INLINE itraversed #-}

instance FunctorWithIndex Int NonEmpty
instance FoldableWithIndex Int NonEmpty
instance TraversableWithIndex Int NonEmpty where
  itraverse = itraverseOf traversed
  {-# INLINE itraverse #-}

instance FunctorWithIndex () Maybe where
  imap f = fmap (f ())
  {-# INLINE imap #-}
instance FoldableWithIndex () Maybe where
  ifoldMap f = foldMap (f ())
  {-# INLINE ifoldMap #-}
instance TraversableWithIndex () Maybe where
  itraverse f = traverse (f ())
  {-# INLINE itraverse #-}

-- | The position in the 'Seq' is available as the index.
instance FunctorWithIndex Int Seq where
  imap = mapWithIndex
instance FoldableWithIndex Int Seq where
  ifoldMap f = Data.Foldable.fold . mapWithIndex f
  ifoldr = foldrWithIndex
  ifoldl f = foldlWithIndex (flip f)
  {-# INLINE ifoldl #-}
instance TraversableWithIndex Int Seq where
-- The next version of containers will probably offer traverseWithIndex;
-- when that comes out, it should be used for this.
  itraverse f = sequenceA . mapWithIndex f

instance FunctorWithIndex Int Vector where
  imap = V.imap
  {-# INLINE imap #-}
instance FoldableWithIndex Int Vector where
  ifoldr = V.ifoldr
  {-# INLINE ifoldr #-}
  ifoldl = V.ifoldl . flip
  {-# INLINE ifoldl #-}
  ifoldr' = V.ifoldr'
  {-# INLINE ifoldr' #-}
  ifoldl' = V.ifoldl' . flip
  {-# INLINE ifoldl' #-}
instance TraversableWithIndex Int Vector where
  itraversed = traversed
  {-# INLINE itraversed #-}

instance FunctorWithIndex Int IntMap
instance FoldableWithIndex Int IntMap
instance TraversableWithIndex Int IntMap where
#if MIN_VERSION_containers(0,5,0)
  itraverse = IntMap.traverseWithKey
#else
  itraverse f = sequenceA . IntMap.mapWithKey f
#endif
  {-# INLINE [0] itraverse #-}

{-# RULES
"itraversed -> mapIntMap"    itraversed = sets IntMap.map               :: ASetter (IntMap a) (IntMap b) a b;
"itraversed -> imapIntMap"   itraversed = isets IntMap.mapWithKey       :: AnIndexedSetter Int (IntMap a) (IntMap b) a b;
"itraversed -> foldrIntMap"  itraversed = foldring IntMap.foldr         :: Getting (Endo r) (IntMap a) a;
"itraversed -> ifoldrIntMap" itraversed = ifoldring IntMap.foldrWithKey :: IndexedGetting Int (Endo r) (IntMap a) a;
 #-}

instance FunctorWithIndex k (Map k)
instance FoldableWithIndex k (Map k)
instance TraversableWithIndex k (Map k) where
#if MIN_VERSION_containers(0,5,0)
  itraverse = Map.traverseWithKey
#else
  itraverse f = sequenceA . Map.mapWithKey f
#endif
  {-# INLINE [0] itraverse #-}

{-# RULES
"itraversed -> mapMap"    itraversed = sets Map.map               :: ASetter (Map k a) (Map k b) a b;
"itraversed -> imapMap"   itraversed = isets Map.mapWithKey       :: AnIndexedSetter k (Map k a) (Map k b) a b;
"itraversed -> foldrMap"  itraversed = foldring Map.foldr         :: Getting (Endo r) (Map k a) a;
"itraversed -> ifoldrMap" itraversed = ifoldring Map.foldrWithKey :: IndexedGetting k (Endo r) (Map k a) a;
 #-}

instance (Eq k, Hashable k) => FunctorWithIndex k (HashMap k)
instance (Eq k, Hashable k) => FoldableWithIndex k (HashMap k)
instance (Eq k, Hashable k) => TraversableWithIndex k (HashMap k) where
  itraverse = HashMap.traverseWithKey
  {-# INLINE [0] itraverse #-}

{-# RULES
"itraversed -> mapHashMap"    itraversed = sets HashMap.map               :: ASetter (HashMap k a) (HashMap k b) a b;
"itraversed -> imapHashMap"   itraversed = isets HashMap.mapWithKey       :: AnIndexedSetter k (HashMap k a) (HashMap k b) a b;
"itraversed -> foldrHashMap"  itraversed = foldring HashMap.foldr         :: Getting (Endo r) (HashMap k a) a;
"itraversed -> ifoldrHashMap" itraversed = ifoldring HashMap.foldrWithKey :: IndexedGetting k (Endo r) (HashMap k a) a;
 #-}

instance FunctorWithIndex r ((->) r) where
  imap f g x = f x (g x)
  {-# INLINE imap #-}

instance FunctorWithIndex i (Level i) where
  imap f = go where
    go (Two n l r) = Two n (go l) (go r)
    go (One i a)   = One i (f i a)
    go Zero        = Zero
  {-# INLINE imap #-}

instance FoldableWithIndex i (Level i) where
  ifoldMap f = go where
    go (Two _ l r) = go l `mappend` go r
    go (One i a)   = f i a
    go Zero        = mempty
  {-# INLINE ifoldMap #-}

instance TraversableWithIndex i (Level i) where
  itraverse f = go where
    go (Two n l r) = Two n <$> go l <*> go r
    go (One i a)   = One i <$> f i a
    go Zero        = pure Zero
  {-# INLINE itraverse #-}

instance FunctorWithIndex i (Magma i t b) where
  imap f (MagmaAp x y)    = MagmaAp (imap f x) (imap f y)
  imap _ (MagmaPure x)    = MagmaPure x
  imap f (MagmaFmap xy x) = MagmaFmap xy (imap f x)
  imap f (Magma i a)      = Magma i (f i a)
  {-# INLINE imap #-}

instance FoldableWithIndex i (Magma i t b) where
  ifoldMap f (MagmaAp x y)   = ifoldMap f x `mappend` ifoldMap f y
  ifoldMap _ MagmaPure{}     = mempty
  ifoldMap f (MagmaFmap _ x) = ifoldMap f x
  ifoldMap f (Magma i a)     = f i a
  {-# INLINE ifoldMap #-}

instance TraversableWithIndex i (Magma i t b) where
  itraverse f (MagmaAp x y)    = MagmaAp <$> itraverse f x <*> itraverse f y
  itraverse _ (MagmaPure x)    = pure (MagmaPure x)
  itraverse f (MagmaFmap xy x) = MagmaFmap xy <$> itraverse f x
  itraverse f (Magma i a)      = Magma i <$> f i a
  {-# INLINE itraverse #-}

instance FunctorWithIndex i f => FunctorWithIndex [i] (Free f) where
  imap f (Pure a) = Pure $ f [] a
  imap f (Free s) = Free $ imap (\i -> imap (f . (:) i)) s
  {-# INLINE imap #-}

instance FoldableWithIndex i f => FoldableWithIndex [i] (Free f) where
  ifoldMap f (Pure a) = f [] a
  ifoldMap f (Free s) = ifoldMap (\i -> ifoldMap (f . (:) i)) s
  {-# INLINE ifoldMap #-}

instance TraversableWithIndex i f => TraversableWithIndex [i] (Free f) where
  itraverse f (Pure a) = Pure <$> f [] a
  itraverse f (Free s) = Free <$> itraverse (\i -> itraverse (f . (:) i)) s
  {-# INLINE itraverse #-}

instance Ix i => FunctorWithIndex i (Array i) where
  imap f arr = Array.listArray (Array.bounds arr) . fmap (uncurry f) $ Array.assocs arr
  {-# INLINE imap #-}

instance Ix i => FoldableWithIndex i (Array i) where
  ifoldMap f = foldMap (uncurry f) . Array.assocs
  {-# INLINE ifoldMap #-}

instance Ix i => TraversableWithIndex i (Array i) where
  itraverse f arr = Array.listArray (Array.bounds arr) <$> traverse (uncurry f) (Array.assocs arr)
  {-# INLINE itraverse #-}

instance FunctorWithIndex i f => FunctorWithIndex [i] (Cofree f) where
  imap f (a :< as) = f [] a :< imap (\i -> imap (f . (:) i)) as
  {-# INLINE imap #-}

instance FoldableWithIndex i f => FoldableWithIndex [i] (Cofree f) where
  ifoldMap f (a :< as) = f [] a `mappend` ifoldMap (\i -> ifoldMap (f . (:) i)) as
  {-# INLINE ifoldMap #-}

instance TraversableWithIndex i f => TraversableWithIndex [i] (Cofree f) where
  itraverse f (a :< as) = (:<) <$> f [] a <*> itraverse (\i -> itraverse (f . (:) i)) as
  {-# INLINE itraverse #-}

instance (FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (i, j) (Compose f g) where
  imap f (Compose fg) = Compose $ imap (\k -> imap (f . (,) k)) fg
  {-# INLINE imap #-}

instance (FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (i, j) (Compose f g) where
  ifoldMap f (Compose fg) = ifoldMap (\k -> ifoldMap (f . (,) k)) fg
  {-# INLINE ifoldMap #-}

instance (TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (i, j) (Compose f g) where
  itraverse f (Compose fg) = Compose <$> itraverse (\k -> itraverse (f . (,) k)) fg
  {-# INLINE itraverse #-}

instance FunctorWithIndex i m => FunctorWithIndex i (IdentityT m) where
  imap f (IdentityT m) = IdentityT $ imap f m
  {-# INLINE imap #-}

instance FoldableWithIndex i m => FoldableWithIndex i (IdentityT m) where
  ifoldMap f (IdentityT m) = ifoldMap f m
  {-# INLINE ifoldMap #-}

instance TraversableWithIndex i m => TraversableWithIndex i (IdentityT m) where
  itraverse f (IdentityT m) = IdentityT <$> itraverse f m
  {-# INLINE itraverse #-}

instance (FunctorWithIndex i f, FunctorWithIndex j g) => FunctorWithIndex (Either i j) (Product f g) where
  imap f (Pair a b) = Pair (imap (f . Left) a) (imap (f . Right) b)
  {-# INLINE imap #-}

instance (FoldableWithIndex i f, FoldableWithIndex j g) => FoldableWithIndex (Either i j) (Product f g) where
  ifoldMap f (Pair a b) = ifoldMap (f . Left) a `mappend` ifoldMap (f . Right) b
  {-# INLINE ifoldMap #-}

instance (TraversableWithIndex i f, TraversableWithIndex j g) => TraversableWithIndex (Either i j) (Product f g) where
  itraverse f (Pair a b) = Pair <$> itraverse (f . Left) a <*> itraverse (f . Right) b
  {-# INLINE itraverse #-}

instance FunctorWithIndex i m => FunctorWithIndex (e, i) (ReaderT e m) where
  imap f (ReaderT m) = ReaderT $ \k -> imap (f . (,) k) (m k)
  {-# INLINE imap #-}

instance FunctorWithIndex i w => FunctorWithIndex (s, i) (TracedT s w) where
  imap f (TracedT w) = TracedT $ imap (\k' g k -> f (k, k') (g k)) w
  {-# INLINE imap #-}

instance FunctorWithIndex [Int] Tree where
  imap f (Node a as) = Node (f [] a) $ imap (\i -> imap (f . (:) i)) as
  {-# INLINE imap #-}

instance FoldableWithIndex [Int] Tree where
  ifoldMap f (Node a as) = f [] a `mappend` ifoldMap (\i -> ifoldMap (f . (:) i)) as
  {-# INLINE ifoldMap #-}

instance TraversableWithIndex [Int] Tree where
  itraverse f (Node a as) = Node <$> f [] a <*> itraverse (\i -> itraverse (f . (:) i)) as
  {-# INLINE itraverse #-}

-------------------------------------------------------------------------------
-- Misc.
-------------------------------------------------------------------------------

skip :: a -> ()
skip _ = ()
{-# INLINE skip #-}

-------------------------------------------------------------------------------
-- Indexed Folds with Reified Monoid
-------------------------------------------------------------------------------

ifoldMapBy :: FoldableWithIndex i t => (r -> r -> r) -> r -> (i -> a -> r) -> t a -> r
ifoldMapBy f z g = reifyMonoid f z (ifoldMap (\i a -> ReflectedMonoid (g i a)))

ifoldMapByOf :: IndexedFold i t a -> (r -> r -> r) -> r -> (i -> a -> r) -> t -> r
ifoldMapByOf l f z g = reifyMonoid f z (ifoldMapOf l (\i a -> ReflectedMonoid (g i a)))

itraverseBy :: TraversableWithIndex i t => (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (i -> a -> f b) -> t a -> f (t b)
itraverseBy pur app f = reifyApplicative pur app (itraverse (\i a -> ReflectedApplicative (f i a)))

itraverseByOf :: IndexedTraversal i s t a b -> (forall x. x -> f x) -> (forall x y. f (x -> y) -> f x -> f y) -> (i -> a -> f b) -> s -> f t
itraverseByOf l pur app f = reifyApplicative pur app (itraverseOf l (\i a -> ReflectedApplicative (f i a)))